Page 554 - Basic College Mathematics with Early Integers

7.3 MEAN, MEDIAN, AND MODE Objectives

Find the Mean of a List
of Numbers.
Objective Finding the Mean
Find the Median of a List
Sometimes we want to summarize data by displaying them in a graph, but some-
of Numbers.
times it is also desirable to be able to describe a set of data, or a set of numbers, by a
single “middle” number.Three such measures of central tendency are the mean, the Find the Mode of a List
median, and the mode. of Numbers.
The most common measure of central tendency is the mean (sometimes called
the “arithmetic mean” or the “average”). Recall that we first introduced finding the
average of a list of numbers in Section 1.7.

The mean (average) of a set of number items is the sum of the items divided by
the number of items.
sum of items
mean =
number of items

Example 1 Finding the Mean Time in an Experiment PRACTICE 1
Find the mean of the follow-
Seven students in a psychology class conducted an experiment on mazes. Each
ing test scores: 87, 75, 96, 91,
student was given a pencil and asked to successfully complete the same maze. The
and 78.
timed results are below:
Student Ann Thanh Carlos Jesse Melinda Ramzi Dayni
Time (Seconds) 13.2 11.8 10.7 16.2 15.9 13.8 18.5

a. Who completed the maze in the shortest time? Who completed the maze in the
longest time?
b. Find the mean time.
c. How many students took longer than the mean time? How many students took
shorter than the mean time?
Solution:
a. Carlos completed the maze in 10.7 seconds, the shortest time. Dayni completed
the maze in 18.5 seconds, the longest time.
b. To find the mean (or average), we find the sum of the items and divide by 7, the
number of items.
13.2 + 11.8 + 10.7 + 16.2 + 15.9 + 13.8 + 18.5
mean =
7
100.1
= = 14.3
7
c. Three students, Jesse, Melinda, and Dayni, had times longer than the mean
time. Four students, Ann, Thanh, Carlos, and Ramzi, had times shorter than the
mean time.
Work Practice 1

Concept Check Estimate the mean of the following set of data:
Answer
5, 10, 10, 10, 10, 15 1. 85.4
Often in college, the calculation of a grade point average (GPA) is a weighted Concept Check Answer
mean and is calculated as shown in Example 2. 10
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